An improved decoupling approximation method for nonlinear granular composites

An improved decoupling approximation is proposed to estimate the spatial average of ∥E∥^β, where ∥E∥ denotes the magnitude of the local electric field E and β (β ≥ 3) is the nonlinear exponent. As an example, we recalculate the nonlinear susceptibilities of weakly nonlinear composites and find that our present results are very close to the simulation data.     

Te-waves guided by arbitrary nonlinear dielectrics bounded by linear media

Considerable interest is currently being devoted to nonlinear propagation in dielectric slab waveguides for integrated optics and millimetric applications. Much of the current work is based on Kerr-like ( E ²) nonlinear media and numerically discussed. We present a exact solution of TE-waves for arbitrary nonlinear dielectric ( |E| ). We applicate this solution to the planar nonlinear optic waveguides and the dispersion relations are given. The results show that the propagation constants are a function of the field magnitude.Supported by deutscher akademischer austauschdienst (DAAD)He is now with Dept. Electrical Engineering, Duisburg University, 4100 Duisburg, Germany     

Thickness dependent optical dispersion parameters and nonlinear optical properties of nanostructured Cr doped CdO thin films

Cr doped CdO thin films were deposited on glass substrates by reactive DC magnetron sputtering with varying film thickness from 250 to 400 nm. XRD studies reveal that the films exhibit cubic structure with preferred orientation along the (2 0 0) plane. The optical transmittance of the films decreases from 92 to 72%, whereas the optical energy band gap of the films decreased from 2.88 to 2.78 eV with increasing film thickness. The Wemple–DiDomenico single oscillator model has been used to evaluate the optical dispersion parameters such as dispersion energy (E_d), oscillator energy (E_o), static refractive index (n_o) and high frequency dielectric constant (ε_∞). The nonlinear optical parameters such as optical susceptibility (χ⁽¹⁾), third order nonlinear optical susceptibility (χ⁽³⁾) and nonlinear refractive index (n₂) of the films were also determined.     

Nonlinear control of the propagation of optical pulses in doped optical fibers

Results of study of nonlinear processes occurring during the propagation of light pulses in optical fibers doped with atoms of rare-earth elements under conditions of atomic coherence and interference are presented. For a three-level Λ scheme of interaction, the linear (χ⁽¹⁾) and nonlinear (χ⁽³⁾) susceptibilities of such a medium are calculated. It is shown that the coefficients of Kerr nonlinearity and nonlinear absorption can reach extremely large values and can be negative. The competition between linear and nonlinear processes in the Λ scheme allows one to obtain compensation regimes when the coefficients of dispersion or absorption of the optical fiber material vanish. The efficient control of the optical properties of such a system over wide limits proves to be possible owing to variations in the parameters of light pulses at the input of the medium. The necessary conditions for realizing regimes with “slow” light, as well as for self-compression of a probing pulse on ultimately small spatial scales in a doped optical fiber, were obtained.     

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_app = E₀ (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_i (r) = C_k r^k (r ≤ a), where r is the radius of the cylindrical inclusion, and C_k, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.     

直流偏置电场下BaTiO３基陶瓷介电常数非线性机理的研究

采用传统固相法制备了Ba_0.6Sr_0.4TiO_３(BST)和BaZr< sub>xTi_１-xO_３(x=0.25，0.3，0.35，0.4)（ＢＺＴ）陶瓷 ，并对其在直流偏置电场下的介电常数非线性行为进行了系统、详细的研究.结果表明，基 于Devonshire的宏观相变理论(phenomenological theory)提出的公式ε_r(app) ε_r(0)=1［1+αε^{３_{r(0)E２ ］1/3和ε(E)=ε1－ε2E2+ε3E4，均可定量地解释BST体系顺电相的介电常数非线性行为，其中εr (app)表示材料在电场下的介电常数，εr(0)表示不加电场即静态下材料 的介电常数，α是非谐性因子，E表示电场强度，ε(E)表示材料在电场下的介电常数，ε１，ε２，ε３分别表示线性、非线性和高阶介电常数. 而对于处于铁电相和居里温度附近的BST体系，则需要考虑铁电畴对介电常数非线性的贡献 ，这种贡献随着外加直流偏置电场强度的增大逐步减小.对于弛豫铁电体BZT体系，即使处于 顺电相，也必须考虑由极性微区的冻结与合并引起的介电常数的下降，极性微区对介电常数 非线性的贡献随着电场强度和温度的上升而有所下降. 关键词： BST x}Ti_１-xO_３')" href="#">BaZr_xTi_１-xO_３ 可调性 介电 常数非线性 直流偏置电场}     

Synthesis of CdZnO thin film as a potential candidate for optical switches

Cadmium doped zinc oxide thin films have been prepared using a thermal decomposition technique. The influence of Cd as a doping agent on the structure, optical and nonlinear optical properties was carefully investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM) and a UV-vis spectrophotometer. A deep correlation has been found between the surface roughness and the optical properties. The roughness is found to deteriorate the nonlinear response, such that the highest nonlinear susceptibility χ⁽³⁾ is obtained for the smoothest layer. The third-order nonlinear susceptibility χ⁽³⁾ has been calculated using the Frumer model, and is estimated to be 3.37×10⁻¹⁰ esu. The dispersion of the refractive index of the prepared thin film is shown to follow the single electronic oscillator model. From the model, the values of oscillator strength (E_d), oscillator energy (E_o) and dielectric constant (ε_∞) have been determined. The conductivity has been measured as a function of the energy of the photons, revealing marginal change at energies below 3.15 eV, while above this value there is a large increase in the conductivity. This suggests that CdZnO is a potential candidate for applications in optical devices such as optical limiter and optical switching.     

Interferometric phase measurements of average field cubeE ω 2 E 2ω *

The method of interferometric measurements of the field cube evolutionE ² E ₂ ^* due to propagation in air and other media was investigated experimentally by the use of a pair of nonlinear crystals. A gas cell with variable pressure turned out to be the most convenient among different methods of changing the phase of the field cube. The phase shift by rad of the field cube in passing through the focus was demonstrated experimentally.     

Electric field dependence of the Curie temperature and microwave absorption in displacive ferroelectrics with impurities II

Expressions for the complex dielectric constant, microwave absorption and the Curie temperature in doped displacive ferroelectrics, subjected to an external electric field are discussed, using the approach made in our previous study. A cross-term of defect parameters with electric field and anharmonic parameters is obtained. The intrinsic parametersB andC are modified by impurity terms. The qualitativeE ² dependence of tan δ is discussed.     

Parametric dispersion and amplification in semiconductor plasmas: Effects of carrier heating

Using the hydrodynamic model of a semiconductor plasma, the influence of carrier heating on the parametric dispersion and amplification has been analytically investigated in a doped III-V semiconductor, viz. n-InSb. The origin of the phenomena lies in the effective second-order optical susceptibility (χ_e⁽²⁾) arising due to the induced nonlinear current density of the medium. Using the coupled-mode theory, the threshold value of pump electric field (|E_0T|_para) and parametric gain coefficient (α_para) are obtained via χ_e⁽²⁾. The relevant experiment has not been performed. Proper selection of the doping level not only lowers |E_0T|_para required for the onset of parametric excitation but also enhances α_para. The carrier heating induced by the intense pump modifies the electron collision frequency and hence the nonlinearity of the medium, which in turn further lowers |E_0T|_para and enhances α_para by a factor of ∼10³ and ∼2×10², respectively. The results strongly suggest that the incorporation of carrier heating by the pump in the analysis leads to a better understanding of parametric processes in solids and gaseous plasmas, which can be of great use in the generation of squeezed states.     

Reversible permittivity of a photosensitive relaxor ferroelectric

The reversible permittivity of barium strontium niobate, a photosensitive relaxor ferroelectric, doped with lanthanum and cerium is investigated in the dark and under illumination with a power density of 0.22 mW/cm². The permittivity is measured under a combined effect of a weak ac electric field at a frequency of 1 MHz and a slowly varying periodic field E _b with an amplitude of ±2.3 kV/cm. It is shown that the illumination significantly increases the permittivity, changes the dependence of the permittivity on the periodic field E _b , and eliminates the possible unipolarity of the crystal, thus significantly improving the reproducibility of the permittivity during repeated measurements.     

Direct detection of carrier traps in Si solar cells after light‐induced degradation

In solar cells fabricated from boron‐doped Cz‐Si wafers minority and majority carrier traps were detected by deep level transient spectroscopy (DLTS) after so‐called “light‐induced degradation” (LID). The DLTS signals were detected from mesa‐diodes with the full structure of the solar cells preserved. Preliminary results indicate metastable traps with energy levels positioned at E_V + 0.37 eV and E_C – 0.41 eV and apparent carrier capture cross‐sections in the 10^–17–10^–18 cm² range. The concentration of the traps was in the range of 10¹²–10¹³ cm^–3. The traps were eliminated by annealing of the mesa‐diodes at 200 °C. No traps were detected in Ga‐doped solar cells after the LID procedure or below the light protected bus bar locations in B‐doped cells. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Creation of electron-positron plasma with superstrong laser field

We present a short review of recent progress in studying QED effects within the interaction of ultra-relativistic laser pulses with vacuum and e ^? e ⁺ plasma. Current development in laser technologies promises very rapid growth of laser intensities in the near future. Two exawatt class facilities (ELI and XCELS, Russia) in Europe are already in the planning stage. Realization of these projects will make available a laser intensity of ～ 10²⁶?W/cm² or even higher. Therefore, discussion of nonlinear optical effects in vacuum are becoming compelling for experimentalists and are currently gaining much attention. We show that, in spite of the fact that the expected field strength is still essentially less than E _S = m ² c ³/e? = 1.32 · 10¹⁶?V/cm, the nonlinear vacuum effects will be accessible for observation at the ELI and XCELS facilities. The most promissory effect for observation is pair creation by a laser pulse in vacuum. It is shown, that at intensities ～ 5 · 10²⁵?W/cm², creation even of a single pair is accompanied by the development of an avalanche QED cascade. There exists a distinctive feature of the laser-induced cascades, as compared with the air showers arising due primarily to cosmic rays entering the atmosphere. In our case the laser field plays not only the role of a target (similar to a nucleus in the case of air showers) but is also responsible for the acceleration of slow particles. It is shown that the effect of pair creation imposes a natural limit for the attainable laser intensity and, apparently, the field strength E ～ E _S is not accessible for a pair-creating electromagnetic field at all.     

Nonlinear refraction and photoinduced birefringence in chlorophosphonazo I doped polymer thin films

The nonlinear refraction and photoinduced birefringence of chlorophosphonazo I (CPA I ) doped PVA thin films were investigated. The single-beam Z-scan measurement showed that CPA I doped PVA thin film possessed a large value of nonlinear refractive index (n₂=1.82×10⁻¹² cm²/W) under a pulse 532 nm excitation, and the mechanism accounting for the process of nonlinear refraction was discussed in term of resonant electronic effect. Moreover, fast and stable molecular reorientation was observed when investigating the photoinduced birefringence of CPA I doped PVA thin film with a CW 532 nm laser as pump light and a CW 650 nm laser as probe light.     

Diagnostic study of the roughness surface effect of zirconium on the third-order nonlinear-optical properties of thin films based on zinc oxide nanomaterials

Zinc oxide (ZnO) and zirconium doped zinc oxide (ZnO:Zr) thin films were deposited by reactive chemical pulverization spray pyrolysis technique on heated glass substrates at 500 °C using zinc and zirconium chlorides as precursors. Effects of zirconium doping agent and surface roughness on the nonlinear optical properties were investigated in detail using atomic force microscopy (AFM) and third harmonic generation (THG) technique. The best value of nonlinear optical susceptibility χ⁽³⁾ was obtained from the doped films with less roughness. A strong third order nonlinear optical susceptibility χ⁽³⁾ = 20.12 × 10⁻¹² (esu) of the studied films was found for the 3% doped sample.     

Antiferromagnetic hall effect nonlinear in the electric current

A new galvanoantiferromagnetic effect is predicted—the Hall effect nonlinear in the electric current, i.e., a potential difference that is transverse to the current and is associated with the antisymmetric contribution to the resistivity tensor, which violates Ohm’s law, for example, of the form Δρij=?Δρji∝LE, where L is the antiferromagnetism vector and E is the electric field. The indicated contribution is characteristic for centrally antisymmetric antiferromagnets and can lead to a Hall field that is quadratic in the current: ΔE ^⊥ ∝ LJ ². Similarly, the effect ΔE ^⊥∝LJ ³ can exist in centrally symmetric antiferromagnets even in a state where the ordinary Hall effect, which is linear in J, is absent (for example, in hematite below the Morin point).     

Third-order nonlinear optical response in double-walled carbon nanotubes

Resonant behavior and magnitudes of third-order nonlinear optical susceptibilities in double-walled carbon nanotubes (DWNTs) have been investigated by means of femtosecond pump-probe spectroscopy with different pump-photon energies. With the selective excitation of the E₂₂ exciton transition of the inner tubes labeled by the chiral vector indices (7,5) and (7,6), the imaginary part of nonlinear susceptibility Imχ⁽³⁾ has shown the resonant enhancement compared with the case of the nonresonant excitation of the specific tube. The nonlinear response signal at the E₂₂ transition energy of the (8,7) tube has been also enhanced for the excitation of the G-band phonon sideband of its E₂₂ transition. This result is consistent with the phonon-mediated nonlinear optical process observed for the E₂₂ transitions in single-walled carbon nanotubes (SWNTs). It has been also found that the values of the figure of merit Im χ⁽³⁾/α (α: absorption coefficient) of the inner tubes in DWNTs are smaller than those of the corresponding SWNTs, which is interpreted in terms of decay time shortening due to the energy relaxation between the inner and outer tubes.     

Two and four photon absorption and nonlinear refraction in undoped,chromium doped and copper doped ZnS quantum dots

The ZnS quantum dots (QDs) with Cr and Cu doping were synthesized by chemical co-precipitation method. The nanostructures of the prepared undoped and doped ZnS QDs were characterized by UV–vis spectroscopy, Transmission electron microscopy (TEM) and X-ray diffraction (XRD). The sizes of QDs were found to be within 3–5 nm range. The nonlinear parameters viz. Two photon absorption coefficient (β₂), nonlinear refractive index (n₂), third order nonlinear susceptibility (χ³) at wavelength 532 nm and Four photon absorption coefficient (β₄) at wavelength 1064 nm have been calculated by Z-scan technique using nanosecond Nd:YAG laser in undoped, Cr doped and Cu doped ZnS QDs. Higher values of nonlinear parameters for doped ZnS infer that they are potential material for the development of photonics devices and sensor protection applications.     

Study of the gain saturation effect on the propagation of dark soliton in Er-doped, Ga5Ge20Sb10S65 chalcogenide fiber amplifier

We study the effect of gain saturation on the propagation of fundamental dark soliton in a nonlinear, dispersive and amplifying medium. The Er^+ 3-doped, Ga₅Ge₂₀Sb₁₀S₆₅ chalcogenide glass is used for dark and erbium doped silicon glass for bright solitons. The numerical simulations show that dark soliton doesn't split to subpulses unlike bright soliton and also the dark soliton is more stable in the presence of gain saturation and gain dispersion effects. So the chalcogenide glasses are suitable for designing all optical devices.     

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=10¹⁶−6×10¹⁶ cm⁻³, ionization energy ε₁≃45 meV) with compensation K=10⁻⁴−10⁻⁵ in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D ⁻ band, which is filled with carriers under the influence of the field E. In fields E<E _q (E _q ≃100–200 V/cm) the carrier motion consists of hops along localized D ⁻ states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε₁); for E>E _q carriers drift along localized D ⁻ states with energy ε∞ε₁−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997)